High-resolution X-ray powder diffractometry enables closely spaced peaks in an X-ray diffraction pattern to be isolated, allowing greater certainty in the identification of phases present in powdered material. The purpose of high-angular resolution methods is to reduce the width of the diffraction lines, which has particular relevance for samples containing a combination of phases with closely spaced peaks, arising from similar crystal plane spacings. High-resolution is also relevant for studying powders with large crystal lattice parameters that have many peaks. The peaks in a powder diffractogram are broadened from several contributions; namely sample related aspects such as crystallite size and strain effects, instrumental contributions associated with its geometry and wavelength dispersion.
Current Methods in Powder Diffraction:
The discovery of X-ray scattering from fine powders was pioneered by Debye and Scherrer and the simplest geometry is generally termed the Debye-Scherrer camera. It operates by placing a small sample in the centre of a cylinder of film (or a position sensitive detector). The resolution can be increased by careful collimation of the incident beam and improving the ratio of the sample diameter to the detector radius. The sample dimensions ideally should be small since, as the radius is increased, the path length is increased, with the consequent loss in collected intensity. Similarly the intensity diminishes with the degree of collimation, since longer slit separations are necessary.
This geometry in its simplest form is unsuitable for high-resolution data collection, because the sample to detector distance needs to be large and the sample to be small. In practice the sample is usually mounted in a capillary or on the outside of a glass fibre resulting in typical sample sizes of 350 μm to 700 μm diameter. Therefore to achieve peak widths less than 0.10 would require radii of >200 mm or >400 mm respectively, provided that the incident beam has no divergence and there is no wavelength dispersion and no microstructure broadening.
The favoured method for achieving high-resolution powder diffractometry requires a focusing geometry, which helps to maintain intensity, and can more easily include some degree of monochromatisation. To achieve the focusing condition the sample, the divergent point of the incident beam and convergent point of the scattered beam should lie on the circumference of a focusing circle. This configuration requires a sample bent to the radius of the circle, or one that is very small in comparison with the radius of the focusing circle. The path length and quality of focusing can be difficult to maintain in practice, however it does allow parallel data collection; by placing film or position sensitive counter detectors around the focusing circle. If the sample is flat this focusing condition is not precise enough to achieve high resolution, unless the instrument has very large path lengths.
To overcome the problem of having a flat sample, the incident and scattered beams can be kept symmetrically related, so that the incident angle onto the sample is half the scattering angle 2θ can be such that the focusing condition is maintained. This is the basis of the so-called “Bragg-Brentano” arrangement. However, to capture peaks at differing 2θ values, does require rotation of the sample and the detector and therefore the data cannot be collected in parallel. This is suitable for large samples. This geometry becomes problematic at low angles without heavily restricting the incident beam divergence, although this can be done automatically with variable slits linked to the incident angle; effectively maintaining the same area on the sample visible to the incident beam.
Both these latter methods, Seemann-Bohlin and Bragg-Brentano, use a reflection geometry in which the incident X-ray beam and the measured beam leaving the sample are on the same side of the sample, which can be a problem for some low absorbing materials in that the penetration will effectively move the sample off the focusing circle and reduce the resolution. Also the resolution depends strongly upon the focus size and the receiving slit dimension. For a typical diffractometer with a radius of 240 mm and a receiving slit of 0.25 mm, negligible focus size and no wavelength dispersion, a resolution of 0.10 can be achieved.
Significant broadening may occur due to the wavelength spread. To remove some of this wavelength dispersion, e.g. isolating the Kα1 component of the Kα1 Kα2 doublet, requires some level of monochromation. Guinier added a curved single crystal to the Seemann-Bohlin camera to isolate the Kα1 component; and the beam from this was brought to a focus. This gave a very useful moderate- to high-resolution camera.
To improve the wavelength dispersion in the Bragg-Brentano geometry, the convergent focusing can be achieved with a bent single crystal as in the Guinier camera. Since the intrinsic diffraction width of a single crystal is typically 0.0030, the Kα1 component of the Kα1 Kα2 doublet can easily be isolated and focused onto the incident beam slit. The resolution now depends an the size of the slit at or the exactness of the curvature of the collimating crystal. High-resolution is relatively straightforward to achieve in reflection mode, however in transmission mode this is more problematic, because of the difficulty in bending a single crystal to such precision.
Other options in high-resolution also include monochromators in the diffracted beam.
In all cases, the means of improving the resolution requires the instrument to become significantly larger.
The size of the instrument is a very significant consideration when the use of the instrument is considered. There is a considerable need for a relatively small instrument since small instruments can generally be manufactured and transported more easily and they are much easier to fit into existing manufacturing plants.
A further factor that needs to be considered is the ease of setting up the instrument. If the instrument requires very complex setting up and calibration, it is unlikely to be suitable except in a research environment where highly skilled and experienced personnel are available. However, a diffractometer is a very useful instrument also in circumstances where such personnel are not available.
The highest resolutions are achievable using a focussing geometry and a scanning mode, however this typically requires the data to be collected in series rather than parallel.
Ideally the inventors would like to achieve high-resolution, with good intensity, use a reasonable sized sample and keep the measurement time low and the instrument small.